I wouldn't toss out the idea altogether. I did the Honors program at my school, so I'll run through a few of my thoughts on it.
First, as others have asked, will it affect your GPA? It might, but you're the best judge of that. For me, the Honors professors tended to grade significantly harder (especially in terms of quality of writing) than those of my friends not in the program. So yes, it probably brought my GPA down a little - I graduated with about a 3.46, and maybe I could have had more like a 3.7 if I'd taken easier, non-Honors classes, but I'd be surprised if it made the difference between picking up 1390 and being sent to SWO-land for you; it obviously didn't hurt me that much.
Secondly, make sure the Honors classes won't interfere with your scheduling too much. I think I was the second NROTC student to do the Honors program at my school and I know was the second student from my major to do it; I was the first to try to put all three together, and it turned out the programs didn't mesh very well. If you're going to a big school, it shouldn't be too difficult to make it work, but at a small college like the one I went to, class offerings are pretty limited and I wound up having a lot of scheduling conflicts that were sometimes tricky to work through.
Also, as Uncle Fester said, consider what the experience will do for you post-Navy. But additionally, consider what it will do for you IN the Navy. The apparent obvious answer is "nothing" - nobody's ever going to care that you were in Honors in college - but I think there's a lot more to it than that. For example, as I said, the professors in the classes I took held us to pretty high standards in terms of writing and I became a much better writer because of it. That helped me a lot in other classes, probably most notably my CO's ethics class. He was very picky with writing as well and handed out some pretty harsh grades, but I always managed to do well, which made me stand out in my class. And good writing skills will often be very helpful throughout an officer career (or so I've been told repeatedly).
So I guess my recommendation would be to do some research, talk to professors, talk to students, and consider how it'll affect you in the long run. For me, I think the cost-benefit was in my favor.
